Find the area of the shaded region. Round your answer to the nearest hundredth.

12=side length

The area of the shaded region is about — square units.

How do you find the area of the shaded region? Thank you!

Find The Area Of The Shaded Region. Round Your Answer To The Nearest Hundredth.12=side LengthThe Area

Answers

Answer 1

Answer:

Step-by-step explanation:

Divide 360 by the number of sides in a regular polygon to find θ

θ = 360/5 = 72°

Use law of cosines to find the radius of the circle which equals the common length sides of the isosceles triangle

12² = R² + R² - 2•R•Rcos72

12² = 2R² - 2R²cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

The height of the isosceles triangle is

h = Rcos(θ/2) = 10.2078cos(72/2) = 8.258291...

The shaded area is the area of the circle minus the area of the pentagon.

A = π(104.1993) - 5(½(12)(8.258291))

A = 327.35200... - 247.74874...

A = 79.6032575...

A = 79.60 units²

Find The Area Of The Shaded Region. Round Your Answer To The Nearest Hundredth.12=side LengthThe Area
Answer 2

The Area of the shaded region is A = 79.60 units²

What is law of Cosine?

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle that separates them by two.

Given:

length= 12

So, Divide 360 by the number of sides in a regular polygon

θ = 360/5

θ = 72°

Use law of cosines

12² = R² + R² - 2 x R x Rcos72

12² = 2R² - 2R² cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

Thus, the height of the isosceles triangle is

h = R cos(θ/2)

   = 10.2078cos(72/2)

   = 8.258291...

and, the shaded area is

A = π(104.1993) - 5(½)(12)(8.258291))

A = 327.35200 - 247.74874

A = 79.6032575

A = 79.60 units²

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Craig has a job waiting tables where he earns $3.45 per hour plus tips. Craig earned $73.68 in tips during his shift yesterday.

If x represents the number of hours Craig worked yesterday, which of the following equations can be used to find the amount of money Craig earned yesterday?
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Answers

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Answer:

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Step-by-step explanation:

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If 20% of the students are boys then 80% are girls

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Answer:

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Step-by-step explanation:

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For a project in his Geometry class, Ryan uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then walks 3.4 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Answers

9514 1404 393

Answer:

  4.82 m

Step-by-step explanation:

The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.

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Answers

What is the options?

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Answers

Answer:

-b = 14

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Step-by-step explanation:

For b

50/100=b/28 cross-multiply

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For n

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Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Answer:

Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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Answers

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

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(b) Notice that x=0.5 meter when θ = 45o. By approximately how many radians should you increase θ if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation.

Answers

The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:

Initial triangle

[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)

Final triangle

[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)

By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)

By (1), we simplify the expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)

If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:

[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)

Then, we reduce (3b) into an entirely algebraic expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)

Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].

Now we clear [tex]\Delta \theta[/tex] within the formula:

[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex]  (5)

If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:

[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]

[tex]y_{2} \approx 0.545[/tex]

[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]

[tex]\Delta \theta = 0.095[/tex]

As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

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Answer:

Step-by-step explanation:

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Angle ABC And BCA a are complementary angle ABC is 85° if angle BCA is named as 3b -7 what could be the value of b?

Answers

Complementary angles add to 90 degrees

Therefore,

angle ABC + angle BCA = 90

But, angle BCA = 3b - 7

and angle ABC = 85

Therefore,

85 + 3b - 7 = 90

3b - 7 = 5

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3x-1 over 5 = x+1 over 3

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Answers

Answer:

(3x-1)/5= (x+1)/3

3(3x-1)=5(x+1)

then solve which the final answer will give you x=8

I need to know that answer please help if you can

Answers

Answer:

$180

Step-by-step explanation:

y = 30x +150

30(1) + 150

= 180

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Answers

Answer:

1,000

Step-by-step explanation:

10 x 10 x 10 = 1,000

1000

Step-by-step explanation:

10³

=10×10×10

1000

Solve the inequality 10y−3(y+2)>2y+4, and write the solution in interval notation.

Answers

Step-by-step explanation:

10y - 3(y + 2) > 2y + 4

10y - 3y - 6 > 2y + 4

(10 - 3 - 2)y > 4 + 6

5y > 10

y > 10/5

y > 2

[tex] \: [/tex]

Solution → y > 2

Interval Notation → [tex] \lang 2 , \infty\rang[/tex]

The solution in interval notation is: (2, ∞)

To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:

Step 1: Distribute the -3 on the left side of the inequality:

10y - 3y - 6 > 2y + 4

Step 2: Combine like terms:

(10y - 3y) - 6 > 2y + 4

7y - 6 > 2y + 4

Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:

7y - 2y - 6 > 2y - 2y + 4

5y - 6 > 4

Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:

5y - 6 + 6 > 4 + 6

5y > 10

Step 5: Finally, solve for y by dividing both sides by 5:

y > 10/5

y > 2

The solution to the inequality is y > 2. Now, let's write it in interval notation.

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Give the digits in the hundred thousands place and the ten thousands place.
746,089

Answers

Answer:

Hundred thousands - 7

Ten Thousands- 4

Step-by-step explanation:

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